Atkin-Lehner |
2- 3+ 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
128832bf |
Isogeny class |
Conductor |
128832 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5203968 |
Modular degree for the optimal curve |
Δ |
-1.2837183029611E+21 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 11- -2 -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2384271,980823249] |
[a1,a2,a3,a4,a6] |
Generators |
[21345337:-2299120752:50653] |
Generators of the group modulo torsion |
j |
91489328511191062832/78351947202214719 |
j-invariant |
L |
2.6661571703264 |
L(r)(E,1)/r! |
Ω |
0.099279657326669 |
Real period |
R |
13.427509869311 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000049416 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128832n1 32208d1 |
Quadratic twists by: -4 8 |